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Computability and Complexity

Foundations and Tools for Pursuing Scientific Applications

  • Textbook
  • May 2024

Overview

Authors:
  1. Rod Downey

    1. School of Mathematics and Statistics, Victoria University, Wellington, New Zealand

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Provides a uniquely concise introduction to these subjects
  • Includes numerous examples and exercises
  • Progresses from general to deeper models of computability

Part of the book series: Undergraduate Topics in Computer Science (UTICS)

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Keywords

  • Finite automata
  • NP-completeness
  • Parameterized complexity
  • Reducability
  • Recursion
  • Structural complexity

About this book

This is a book about computation, something which is ubiquitous in the modern world. More precisely, it examines computability theory and computational complexity theory. Computability theory is the part of mathematics and computer science which seeks to clarify what we mean by computation or algorithm. When is there a computational solution possible to some question? How can we show that none is possible? How computationally hard is the question we are concerned with? Arguably, this area lead to the development of digital computers. (Computational) complexity theory is an intellectual heir of computability theory. Complexity theory is concerned with understanding what resources are needed for computation, where typically we would measure the resources in terms of time and space. Can we perform some task in a feasible number of steps? Can we perform some algorithm with only a limited memory? Does randomness help? Are there standard approaches to overcoming computational difficulty?

Authors and Affiliations

  • School of Mathematics and Statistics, Victoria University, Wellington, New Zealand

    Rod Downey

About the author

Rodney Downey is an Emeritus Professor at Victoria University of Wellington, NZ. He is the co-author of the Springer books, Fundamentals of Parameterized Complexity, and Algorithmic Randomness and Complexity.  He has won many prizes for his work, including (twice) the Shoenfield Prize for writing, as well as the Rutherford Medal, New Zealand’s premier science award.

Bibliographic Information

  • Book Title: Computability and Complexity

  • Book Subtitle: Foundations and Tools for Pursuing Scientific Applications

  • Authors: Rod Downey

  • Series Title: Undergraduate Topics in Computer Science

  • Publisher: Springer Cham

  • eBook Packages: Computer Science, Computer Science (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024

  • Softcover ISBN: 978-3-031-53743-1Due: 11 June 2024

  • eBook ISBN: 978-3-031-53744-8Due: 11 June 2024

  • Series ISSN: 1863-7310

  • Series E-ISSN: 2197-1781

  • Edition Number: 1

  • Number of Pages: XXVIII, 346

  • Number of Illustrations: 17 b/w illustrations

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